I'm assuming you have a 535 here; no other E34 has an integrated trans cooler and radiator.
You won't lose much ATF by disconnecting the lines from the fittings; the cooler is quite small. It'll also be a good chance to see how the fluid is doing and if it merits considering a fluid change (if the car's had regular 15k fluid/filter changes on the trans, and you're getting to the next 15k mark, it'd be a good idea to change it while you're in there).
Install the new radiator and run the car/bleed the cooling system. Get it up to operating temperature by driving the car around and then check the trans fluid level with the car running. The 4hp is an easy trans to service; the more difficult one is the 5hp-30 and variants with the so called "lifetime" (aka 70k) fluid, which requires a specific operating temp to correctly fill.
Use cool blue. Any dexron III / mercon compatible is fine for the trans, or get redline D4 if you're a big spender
best, whit